Numerical adaptive learning control scheme for discrete-time non-linear systems

In this study, a novel numerical adaptive learning control scheme based on adaptive dynamic programming (ADP) algorithm is developed to solve numerical optimal control problems for infinite horizon discrete-time non-linear systems. Using the numerical controller, the domain of definition is constrained to a discrete set that makes the approximation errors always exist between the numerical controls and the accurate ones. Convergence analysis of the numerical iterative ADP algorithm is developed to show that the numerical iterative controls can make the iterative performance index functions converge to the greatest lower bound of all performance indices within a finite error bound under some mild assumptions. The stability properties of the system under the numerical iterative controls are proved, which allow the present iterative ADP algorithm to be implemented both on-line and off-line. Finally, two simulation examples are given to illustrate the performance of the present method.